Robert Oehmke
Quentin F. Stout

Computer Sciece and Engineering, University of Michigan

**Abstract:**
We have developed a flexible tool for efficient adaptive
mesh refinement on a sphere.
Adaptive mesh refinement allows one to concentrate computational resources
on regions of interest, and by extending to spheres we have
extended their applicability to climatology and
other large scale planetary phenomena.
Further, our system can provide adaptation on far more general shapes,
and gridding such as the cubed sphere.

Adaptive mesh refinement is an important technique for saving computational resources when modeling multi-scale phenomena. Rather than using a uniform grid, which would have to be at the resolution of the smallest feature of interest, adaptive grids permit one to use a fine resolution where it is needed, and a coarser resolution elsewhere. This can result in significant time and space savings over simply using a uniform grid.

One of the applications of this work involves the CSEM project to predict geomagnetic storms. These space weather events, which can damage satellites, astronauts, and power lines, are caused by solar coronal mass ejections. To predict these storms, a simulation involving the heliosphere and several different components of the earth's atmosphere is performed. Modeling the earth's atmosphere necessitated our sphere-based adaptive blocks.

Another motivation comes from our collaboration on a project to model atmospheric advection. The adaptation helps track moving features, such as hurricanes. Using static, varying, gridding near the poles can also help reduce some numerical problems.

While our primary focus has been on developing an efficient parallel implementation, our work can be useful on standard (serial) computers as well. Further, it can be helpful even when there is no dynamic adaptation. The block structuring can provide better cache utilization and compiler loop optimizations on each processor, which reduces the run time.

**Keywords:**
adaptive mesh refinement AMR, parallel computing,
geoscience, multi-scale modeling, regular grid, geometric decomposition,
adaptive blocks,
high performance computing, supercomputing

**Complete paper.**
This paper appears in *Proc. 10th SIAM Conf. Parallel Processing for
Scientific Computing*, 2001.

- My work in computational science: papers and an overview of research. Several of the papers describe research utilizing adaptive blocks.
- My work in parallel computing: papers, and an overview of research
- General parallel computing: an explanation of parallel computing, a tutorial, Parallel Computing 101, and a list of parallel computing resources

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